Q: A circuit contains a battery with emf $$\varepsilon = 12\ \text{V}$$ and internal resistance $$r = 0.5\ \Omega$$, connected to a $$5.5\ \Omega$$ load. What is the current in the circuit?

$$I = \frac{12}{5.5 + 0.5} = 2.0\ \text{A}$$

Q: Which of the following best describes the time constant $$\tau in an RC $$circuit?

$$\tau = RC$$, the time to reach 63.2\%$ of the final voltage when charging a capacitor.

Q: A $$1800\ \text{W}$$ toaster, $$1400\ \text{W}$$ frying pan, and $$75\ \text{W}$$ lamp are plugged into a $$120\ \text{V}$$, $$15\ \text{A}$$ circuit in parallel. What is the total current drawn, and will the fuse blow?

Total current is $$28\ \text{A}$$; the fuse will blow.

Question 1

Given three resistors $$R_1 = 100$$\ \Omega$$, R_2$ = 2.5\ 	ext{k}\Omega$$, and $$R_3 = 4.0$$\ 	ext{k}\Omega$$ connected in series, what is the equivalent resistance R_s$ of the combination?

Accepted Answer

$$R_s = 6600\ \Omega$$

Question 2

For the same resistors as above, if they are connected in parallel, what is the equivalent resistance $$R_p$$?

Accepted Answer

$$R_p = 93.9\ \Omega$$

Question 3

A 48.0 V battery is connected to a $$24.0\ \Omega$$ and a $$96.0\ \Omega$$ resistor in series. What is the current through each resistor?

Accepted Answer

$$I = 0.400\ 	ext{A}$$

Question 4

Which of the following statements about resistors in parallel is correct?

Accepted Answer

The voltage across each resistor is the same.

Question 5

A battery has an emf $$\varepsilon$$ and internal resistance $$r. If a $$current $$I is $$drawn, what is the terminal voltage $$V_{ab}$$?

Accepted Answer

$$V_{ab} = \varepsilon - Ir$$

Question 6

A 3.00 V lithium cell with internal resistance $$2.00\ \Omega$$ supplies $$0.300\ 	ext{mA}. $$What is the terminal voltage?

Accepted Answer

$$V_{ab} = 3.00\ 	ext{V}$$

Question 7

If the terminal voltage of a battery drops by $$2.00\ 	ext{V}$$ when the current increases by $$5.00\ 	ext{A}$$, what is the internal resistance?

Accepted Answer

$$r = 0.400\ \Omega$$

Question 8

Which of the following is Kirchhoff’s junction rule?

Accepted Answer

The sum of all currents entering a junction equals the sum of all currents leaving the junction.

Question 9

In the Wheatstone bridge, when the galvanometer shows zero current, what is the relationship for the unknown resistance $$R_x$$?

Accepted Answer

$$R_x = R_3$ \frac{R_2$}{R_1$}$$

Question 10

A heart pacemaker fires 72 times per minute, charging a $$25.0\ 	ext{nF}$$ capacitor to $$0.632 of $$its full voltage each time. What is the resistance in the circuit?

Accepted Answer

$$R = 33.3\ 	ext{M}\Omega$$

Question 11

Which of the following best describes the function of an ideal voltmeter?

Accepted Answer

It measures the potential difference between two points and has infinite resistance.

Question 12

In an RC circuit, what is the voltage across the capacitor as it charges over time?

Accepted Answer

$$V = \varepsilon (1 - e$$^{-t/RC}$$)$$

Question 13

Which of the following is true about the current in a series circuit containing three resistors?

Accepted Answer

The current is the same through all three resistors.

Question 14

A circuit contains a battery with emf $$\varepsilon = 12\ 	ext{V}$$ and internal resistance $$r = 0.5\ \Omega$$, connected to a $$5.5\ \Omega$$ load. What is the current in the circuit?

Accepted Answer

$$I = \frac{12}{5.5 + 0.5} = 2.0\ 	ext{A}$$

Question 15

Which of the following is a correct sign convention for applying Kirchhoff’s loop rule when traversing a resistor in the direction of current?

Accepted Answer

$$-IR$$

Question 16

A galvanometer is used in which of the following instruments?

Accepted Answer

Ammeter, voltmeter, and Wheatstone bridge

Question 17

Which of the following best describes the time constant $$	au in an RC $$circuit?

Accepted Answer

$$	au = RC$$, the time to reach 63.2\%$ of the final voltage when charging a capacitor.

Question 18

A $$1800\ 	ext{W}$$ toaster, $$1400\ 	ext{W}$$ frying pan, and $$75\ 	ext{W}$$ lamp are plugged into a $$120\ 	ext{V}$$, $$15\ 	ext{A}$$ circuit in parallel. What is the total current drawn, and will the fuse blow?

Accepted Answer

Total current is $$28\ 	ext{A}$$; the fuse will blow.

Circuits and DC Instruments: Series & Parallel Resistors, EMF, Kirchhoff’s Rules, Measuring Devices, Wheatstone Bridge, and RC Circuits

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